The invention relates to the optimization of active system properties based on observed data, and in particular to an active sonar system which selects the optimum waveform for transmission based on the observed scattering properties of the ocean.
Reverberation is often the limiting noise in the performance of active sonars. It results from the reflection of the transmitted sonar waveform from the multitude of boundaries, inhomogeneities, and particles in the ocean medium, collectively referred to as scatterers. Volume reverberation is the result of scatterers distributed in the volume, or body, of the ocean such as marine life and particles. Surface reverberation is produced by scatterers on the sea surface, such as the non-uniformities produced by wave motion. The scatterers spread the transmitted waveform in both frequency (Doppler) and time (range). The spreading of the transmitted energy in time is primarily due to multipath propagation to and from the scatterers. One cause of frequency spreading is the motion of the scatterers relative to the sonar. In many cases, the frequency spreading is due largely to the fact that scattered energy reaching the receiver from different arrival angles have different Doppler shifts resulting from the sonar platform motion. This induces a spread in frequency related to the angular spread of the reverberation returns.
The amount which the environment spreads the transmitted waveform in time and frequency is expressed in terms of the reverberation scattering function, (S(.omega.,.tau.), as described, for example, in Detection, Estimation, and Modulation Theory, by H. L. Van Trees, Part III, J. Wiley and Sons, 1971, and "Digital Signal Processing for Sonar," W. R. Knight, R. G. Pridham and Steven M. Kay, Proceedings of the IEEE, Vol. 69, No. 11, November, 1981, pages 1451-1506.
When reverberation is the dominant source of noise, the detectability of low Doppler targets is greatly reduced. Most active sonar systems utilize a matched filter receiver to detect signals. The matched filter receiver is designed for use with spectrally white stationary noise, but is often used in situations where the noise is non-stationary because of its simplicity. Waveform design is used to improve the performance of the matched filter receiver in reverberation (which is spectrally non-stationary and non-white). A common type of waveform used in active sonars for reverberation-limited environments is the frequency hopped waveform, which consists of a sequence of contiguous single frequency subpulses or "chips" in which the subpulse frequency varies from subpulse to subpulse.
The objective of waveform design is to adjust the distribution of the transmitted signal energy in time and frequency to reduce the reverberation power at the receiver output. This is done based upon a characteristic of waveforms known as the ambiguity function A(.omega.,.tau.), which plots the power at the output of the matched filter for a point target as a function of range, .tau., an Doppler, .omega., relative to the range-Doppler values to which the filter is matched, as described, for example, in the reference. "Characterizing the Radar Ambiguity Function," Auslander, L. and Tolimieri, R., IEEE Transaction on Information Theory, Vol. IT-30, No. 6, Nov. 1986, pages 832-836. The goal of the design procedure is to select waveforms with minimal response to the reverberation, while still preserving the response to the low Doppler signal return. This corresponds to producing a waveform whose ambiguity function has minimal overlap with the reverberation scattering function. See, for example, the reference "On Sonar Signal Analysis," Glisson, T. H.; Black, C. I.; Sage, A. P.; IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-6, No. 1, Jan. 1970, pages 37-49.
For example, if the scattering function consists of a narrow strip along the time axis of the range-Doppler surface, it is desirable to concentrate the sidelobes of the ambiguity function outside this narrow strip. The design of the frequency-hop codes is usually either an exhaustive computer search or a restrictive finite algebra procedure, wherein the transmitted waveforms are designed in advance for an assumed situation. See, for example, the references "A Study of a Class of Detection Waveforms Having Nearly Ideal Range-Doppler Ambiguity Properties," Costas, J. P., Proc. IEEE, Vol. 72, No. 8, August 1984, pages 996-1009; "Construction and Properties of Costas Arrays," Proc. IEEE, Vol 72, No. 9, September 1984, pages 1143-1163. However, insofar as is known to applicants, there is heretofore no systematic method for constructing a suitable waveform based on any arbitrary scattering function for the channel.
In the past, the primary application for scattering function estimation has been the application to communication channels. For example, the reference "Some Techniques for the Instantaneous Real-Time Measurement of Multipath and Doppler Spread," Bello, P. A., IEEE Transactions on Communication Technology, Vol. 13, No. 3, September 1956, pages 285-292, concentrates on the communication problem where the signal transmitted is a CW carrier that is modulated with the information. In that reference, the carrier is used as the primary signal for evaluating the channel spreading. The results of that work do not apply to applications such as active sonars employing frequency hopped waveforms which do not employ a carrier signal which may be exploited to measure the channel scattering function.
Other prior work is described in "Scattering Function Estimation," Gaardner, N. T., IEEE Transactions on Information Theory, Vol IT-14, No. 5, September 1968. In that reference, the channel is treated as a random time varying linear filter, which is estimated using a bank of linear filters followed by a square law detector, followed by another linear filter. The estimate is an unconstrained linear operation that requires that the transmitted signal have sufficient energy and sufficient time and frequency spread (larger than the correlation in time and in frequency of the random filter) so that the filter can resolve all the correlated filter variations in both time and frequency. The results only provide the properties of the filters in the cascade rather than solutions for the filter transfer functions in terms of the ambiguity function of the input.
An object of the invention is to provide a channel adaptive sonar wherein the channel scattering function is measured and a waveform is selected which has an ambiguity function which minimally overlaps the measured scattering function.